Prof. Colin Lambert and Prof. Peter NealASMA JAZZA M ALANAZY2022-06-062019-11-122022-06-0679437https://drepo.sdl.edu.sa/handle/20.500.14154/67807The study presents the Landauer formula and Green’s function approach for analysing the scattering processes in a system attached to infinite one-dimensional leads. The study involves the calculation of the retarded Green’s function in which the simple formula of a one-dimensional tight binding chain in presented. The study involves mathematical aspects of solving the Schrodinger equation in open systems with a view to developing new conceptual approaches to scattering theory. Efficient schemes to obtain scattering matrices from mean-field Hamiltonians are developed and these are implemented in new numerical codes..104enThesis